Let's take a look at how we might write a function like `map` the (pure) functional way in a language like JS:

    const head = ([x, ...xs]) => x;
    const tail = ([x, ...xs]) => xs;
    
    const map = (list, fn) => {
      if (list.length === 0) {
        return [];
      } else {
        return [fn(head(list)), ...map(tail(list), fn)];
      }
    };
    
    map([1, 2, 3], x => x + 1); // [2, 3, 4]

We're not keeping track of any state here. Using recursion you don't need to keep track of the current element in the list for example (when you run this on a physical machine it will of course, but not at the conceptual level).